How can you summon an ender pearl that will teleport you?

Your command worked for me.

After summoning the ender pearl, when you run the /data command, make sure it is selecting the nearest ender pearl. You can check if it's Owner tag matches yours by using /data get entity @e[type=minecraft:ender_pearl,limit=1,sort=nearest] Owner and /data get entity @s UUID

If you are summoning many ender pearls in a small area, it might be that you are selecting the wrong one. You can use:

execute as @e[type=ender_pearl,distance=..5] run data modify entity @s Owner set from entity @p UUID

This will make all ender pearls within a 5 block spherical radius of the execution point set their Owner to the nearest player's UUID.